The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$7.50$, and bags of cookies cost $$4.00$, and sales equaled $$51.00$ in total. There were $7$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Answer: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${7.5x+4y = 51}$ ${y = x+7}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+7}$ for $y$ in the first equation. ${7.5x + 4}{(x+7)}{= 51}$ Simplify and solve for $x$ $ 7.5x+4x + 28 = 51 $ $ 11.5x+28 = 51 $ $ 11.5x = 23 $ $ x = \dfrac{23}{11.5} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+7}$ to find $y$ ${y = }{(2)}{ + 7}$ ${y = 9}$ You can also plug ${x = 2}$ into $ {7.5x+4y = 51}$ and get the same answer for $y$ ${7.5}{(2)}{ + 4y = 51}$ ${y = 9}$ $2$ bags of candy and $9$ bags of cookies were sold.